Alright, say I have a portfolio that yields 8% per year. It consists of stocks and bonds.


I want the portfolio to consist of ~ 80% stocks (closer to 9% annual return)

and ~ 20% bonds (clkoser to 3% annual return)




I want a portfolio that consists of a ratio close to that and comes out to 8% annual return over all.


What % yield does each have to give, and what percent of the portfolio must each be.

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Sorry if the wording makes it a bit hard to understand. I'll try to clarify if need me to/are willing to help.


Will tip fg for quality help. Ty.

ok read up on mvo and capm

0.2*0.03+0.8x=0.09

then

x=0.03+b(0.09-0.03)

get beta

Elaborate please. My burnt out pleb finals week dual overnighter brain can not compute.

maybe you need to elaborate on your question, note:



a portfolio of 80% times 9% return and 20% times 3% return would give you:

0.8*9+0.2*3 = 7.2+0.6 = 7.8 percent return, so if you want to get the 8% you would need to change the balance to achieve

x*9 + (1-x)*3 = 8 -> x*9 + 3 - x*3 = 8 -> x*6 = 5 so x= 5/6 = 0.833... which mean you need 83.333% stocks and 16.667% bonds

is that what you are looking for?

this ^. your above looked fine - just rewriting in case he wishes to vary the % yield as well.


S+B = 1
SC + BD = 8% portfolio yield

S & B are the fraction of the portfolio of stocks and bonds representative.
C is the yield on stocks, and D as a yield on bonds - yields should be % (9% yield or 3% return).

you cannot vary all 4 variables at once.

This post was edited by cialda on Dec 3 2013 06:06pm

grrrr, don't confuse the op even more

if you want to make a general formula it would be
C=yield on item one, with A being the percentage of item one needed
D=yield on item two, with B=1-A being the percentage of item two needed
to achieve a yield Y with C<=Y<=D (assuming C<D) the formula would be
(note if C=D any mix would do)

A*C+(1-A)*D=Y

and only A would be a variable, with C,D,Y being given for the specific target

lol wasnt trying to . but from original post he was talking about possibly varying % yield and % stocks/bonds. so i was just trying to make a formula if he wished to have variable yields and a given portfolio ratio.



This post was edited by cialda on Dec 3 2013 06:23pm

i thought the investment split in stocks and bonds are constant, and you buy and hold bonds with no leverage.

then you just need to calculate beta of the new portfolio or use a leveraged position on a market portfolio although you didn't give any info on your borrowing rate so I assumed it wasn't that

yeah you might wanna elaborate

This was closest to what I was looking for. I really appreciate the input.

This is for a system I'm modeling in Stella. was a bit confused on the math.

I needed 8% return overall on the portfolio or I'd have to re-do a TON of the model. I needed the portfolio to consist of roughly 80% stocks (~9% annual return) 20% bonds (~ 3% annual return) while maintaining an 8% overall return on the portfolio.


Is there a specific term for the process used to derive this? I'd like to be able to do/understand how to derive this for myself in the future.

Basically, you are setting up a system of equations which brmv simplified to a single equation in post # 6. you can input your desired values and solve for an unknown.

what is most important to you the composition being 80%/20%, yields being 9%/3%, or do you have some other desired point?

This post was edited by cialda on Dec 4 2013 05:45pm